Permanence of moment estimates for p-products of convex bodies

Abstract

It is shown that two inequalities concerning second and fourth moments of isotropic normalized convex bodies inR n are permanent under forming p-products. These inequalities are connected with a concentration of mass property as well as with a central limit property. An essential tool are certain monotonicity properties of the -function. Introduction. The topic of the present paper originated from and is connected with a version of the central limit theorem in the context of convex bodies in geometry. A normalized convex body K R n is a convex compact set of volume 1 whose centre of mass is at the origin. A normalized convex body is isotropic if its ellipsoid of inertia is a Euclidean ball, i.e., if